Question

what are the agonist and antagonist muscles of the wrist

Answer 1

I think I understand what you intended, there's just some detail confusion in what you're asking. The term "agonist" refers to the primary movement mode of the muscle, whereas the term "antagonist" refers to muscle pairs (or sets of pairs) that work in opposition to each other (i.e.: abductors and adductors, flexors and extensors). Please don't forget that agonist and doesn't mean the same thing as any of those four other terms.

I would argue that the wrist doesn't have a primary mode of movement but the default assumption for most joints is the flexion action. In any case, what you're really needing here are the names and what are the abductors (a movement which brings a part of the anatomy away from the middle sagittal plane of the body) and adductors (a movement which brings a part of the anatomy closer to the middle sagittal plane of the body).

Abductors of the wrist:
Flexor carpi radialis
Extensor carpi radialis longus
Extensor carpi radialis brevis

Adductors of the wrist:
Flexor carpi ulnaris
Extensor carpi ulnaris

As you can see flexors and extensors are mixed, and there are definitely five of them that control wrist movement.

I feel this is as much as this question can be answered, given the generality of what was written. Hope it helps!